In this blog post, I review a recent preprint article by Mirkowska and Salwicki that claims to have proven the Collatz…

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In this blog post, I review a recent preprint article by Mirkowska and Salwicki that claims to have proven the Collatz conjecture—also known as the (3x + 1) problem. Often the Collatz conjecture is used in class as an example for students to see that reasoning about programs can easily become very difficult, since proving the correctness of a very simple program would amount to showing that the Collatz conjecture is true—a more than 80 year old open problem in mathematics.

The authors Mirkowska and Salwicki make use of the tools of algorithmic logic, a field that is closely related to my field of expertise: Hoare’s logic and dynamic logic. In the blog post, I present what I could distill from Mirkowska and Salwicki’s preprint article, and why I am skeptical that they have actually given a proof of the Collatz conjecture.

https://www.drheap.org/articles/2023/can-the-collatz-conjecture-be-proven-or-not/

Keywords: Presburger arithmetic, non-standard interpretations, partial and total correctness, and variants and invariants.

dr. heap Can the Collatz conjecture be proven, or not? – dr. heap We review a recent preprint article about the Collatz conjecture. The Collatz conjecture is a more than eighty years old problem that is still unsolved.

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